An Integrated GMM Shrinkage Approach with Consistent Moment Selection from Multiple External Sources

Interest has grown in analyzing primary internal data by using some independent external aggregated statistics for efficiency gain. However, when population heterogeneity exists, inappropriate incorporation may lead to a biased estimator. With multiple external sources under generalized estimation equations and possibly heterogeneous populations, we propose an integrated generalized moment method that can perform a data-driven selection of valid moment equations from external sources and make efficient parameter estimation simultaneously. Moment equation selection consistency and asymptotic normality are established for the proposed estimator. Further, when the sample sizes of all external sources are large compared to the internal sample size, asymptotically the proposed estimator is more efficient than the estimator based on the internal data only and is oracle-efficient in the sense that it is as efficient as the oracle estimator based on all valid moment equations. Simulation studies confirm the theoretical results and the efficiency of the proposed method empirically. An example is also included for illustration. Supplementary materials for this article are available online.

学界日益关注借助独立外部汇总统计量开展原始内部数据分析，以提升估计效率。然而，当总体存在异质性时，不当的整合方式会得到有偏估计量。针对广义估计方程（generalized estimation equations）框架下的多外部数据源与可能存在的异质性总体，本文提出一种整合型广义矩方法（generalized moment method），可通过数据驱动方式从外部数据源中筛选有效矩方程，并同步实现高效的参数估计。本文证明了所提估计量具备矩方程选择一致性与渐近正态性。进一步，当所有外部数据源的样本量均大于内部样本量时，从渐近性质来看，所提估计量的效率优于仅基于内部数据的估计量，且具备神谕高效性：其效率等同于基于全部有效矩方程的神谕估计量。模拟研究从实证层面验证了本文的理论结果与所提方法的效率优势。本文还附上实例以作阐释。本文的补充材料可在线获取。